It's worth exploring the nature of fat-tails in the current financial markets. See this table below, which shows the length of time since we've seen a single-day market drop of -x% or worse. For example, we just had a -1% drop last week, and average this level of 1-day drop level every 15 days. We last had a -2% drop 20 days ago, and average this level of 1-day drop every 68 days. In this context a -3% drop (last had one in Winter 2018) in a given day is not that extreme, and we can expect at least one (at -3% or worse) within a year.
But something else is clear from this historical data. If on the normal distribution, there would be proportionately wider frequency interval between progressively worse 1-day drops in the market. But with a thicker-tail in reality, there’s proportionately narrower frequency interval between progressively worse 1-day drops in the market.
So in both cases we would see <-1% 1-day drop 5x more often as a <-2% 1-day drop. In fact a -1% market drop is quite frequent in any modeling scenario. And on a normal distribution, we'd see <-4% 1-day drop (last had one in Spring 2017) as much as 45x more often as a <-5% 1-day drop. But in our fat-tail reality, we'd see <-4% 1-day drop only 2x more often as a <-5% 1-day drop!
So in both cases we would see <-1% 1-day drop 5x more often as a <-2% 1-day drop. In fact a -1% market drop is quite frequent in any modeling scenario. And on a normal distribution, we'd see <-4% 1-day drop (last had one in Spring 2017) as much as 45x more often as a <-5% 1-day drop. But in our fat-tail reality, we'd see <-4% 1-day drop only 2x more often as a <-5% 1-day drop!
The risk becomes more rare if we model with a normal distribution (from a 5x interval, to a 45x intervals). But the same risk becomes less rare when we have a fat-tail model (from a 5x interval, to a 2x interval). So in any given year as well, we would see both a -4% and -5% down-days, as more likely versus a few -3% down-days, in the fat-tail model versus the normal model.
Note risks much more extreme than -5% are much more difficult to accurately contrast since the sampling of actual events becomes very sporadic and clumpy around manias, plus regulations such as circuit breakers, collars, bands. For example, we've only had three days where the market fell by -10% or worse (-10% and -12% both in 1929, and -20% in 1987); and more losses between -8% and -9% in the poll below.
For more reading on tail-risk, please see these popular articles (here, here, here).
Note risks much more extreme than -5% are much more difficult to accurately contrast since the sampling of actual events becomes very sporadic and clumpy around manias, plus regulations such as circuit breakers, collars, bands. For example, we've only had three days where the market fell by -10% or worse (-10% and -12% both in 1929, and -20% in 1987); and more losses between -8% and -9% in the poll below.
n7= # of days in history when S&P has fallen betw -7% & -8%— Statistical Ideas (@salilstatistics) June 3, 2019
n8= # of days in history when S&P has fallen betw -8% & -9%
n9= # of days in history when S&P has fallen -9% or worse
which n is largest? n7, n8, n9, or are the all equal?
[solution shown here https://t.co/JRp0WS4SMB]
For more reading on tail-risk, please see these popular articles (here, here, here).
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